1. 1MPES2 LCD - Add and Subtract on Ecole Supérieure de Commerce de Neuchâtel Pierre Marchal 24.09.2015 http://creativecommons.org/licences/by/3.0/ Attribute to: Pierre Marchal (Lycée Jean-Piaget)

2. Objectives of the course By the end of the course, you should be able to: – Perform prime factorization – Find the LCD – Build up fractions with the same denominator – Add & Subtract any type of fractions: fractions with a common denominator fractions with different denominators

3. Least Common Denominator Prime factorization: To find the LCD use factors with the exponents highest Product of primes 2, 3, 5, 7, 11, 13, … all

4. EXAMPLES OF APPLICATION

5. LCD of 20 and 36 20 10 5 1 LCD : 36 18 9 3 1 2  53 2 2 5 2 2 3 3 2 1 2 4   59 LCD : LCD : 180

6. LCD of 18, 54 and 81 18 9 3 1 81 27 9 3 1 2 3 3 3 3 3 3 1 54 27 9 3 1 2 3 3 3 1 LCD :2  3 4 2  81 LCD : LCD : 162

7. Practice 1: Build up denominators

8. Practice 1: Solutions Build up denominators

9. Practice 2: Homework Find Least Common Denominators: 16, 34 18, 25, 27 12, 13, 14 15, 18, 24, 25

10. Practice 3: Homework Find LCD and build up fractions:

11. Add/Subtract - Common Denominators Add the and keep the Don’t forget to numerators denominators reduce

12. Common denominator Add the numerators : 4 + 6 = 10 Keep the denominator: 15 We get : Don’t forget to reduce:

13. Common denominator Subtract the numerators : 27 - 24 = 3 Keep the denominator: 15 We get : Don’t forget to reduce:

14. Add/Subtract –Different Denominators To add and subtract, we the by by the missing This means, we have to to find the LCD build up denominators multiplying factors factor

15. EXAMPLES OF APPLICATION

16. 1.Find the LCD: 4 2 1 2 2 14 7 1 2 7

17. 2.Find the missing factors: Missing Factor : 7 Missing Factor : 2

18. 3.Build up denominators:

19. Exercises Don’t forget your homework for the next course !

20. By the end of this course You are able to : – Perform prime factorization – Find the LCD – Build up fractions with the same denominator – Add & Subtract any type of fractions: fractions with a common denominator fractions with different denominators

21. Any question ?

22. THANKS FOR YOUR ATTENTION Enjoy “Fête des vendanges” but don’t forget to learn your lesson !